Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

The physics of active systems of self-propelled particles, in the regime of a dense liquid state, is an open puzzle of great current interest, both for statistical physics and because such systems appear in many biological contexts. We develop a nonequilibrium mode-coupling theory (MCT) for such systems, where activity is included as a colored noise with the particles having a self-propulsion force f(0) and a persistence time tau(p). Using the extended MCT and a generalized fluctuation-dissipation theorem, we calculate the effective temperature T-eff of the active fluid. The nonequilibrium nature of the systems is manifested through a time-dependent T-eff that approaches a constant in the long-time limit, which depends on the activity parameters f0 and tp. We find, phenomenologically, that this long-time limit is captured by the potential energy of a single, trapped active particle (STAP). Through a scaling analysis close to the MCT glass transition point, we show that tau(a), the alpha-relaxation time, behaves as tau(a) similar to f(0) (-2 gamma), where gamma = 1.74 is the MCT exponent for the passive system. ta may increase or decrease as a function of tp depending on the type of active force correlations, but the behavior is always governed by the same value of the exponent g. Comparison with the numerical solution of the nonequilibrium MCT and simulation results give excellent agreement with scaling analysis.